

A294651


Least possible value for the highest denominator in the decomposition of unity as a sum of different unitary fractions the greatest of which is 1/n.


2



1, 6, 15, 20, 24, 28, 33, 40, 48, 52, 65, 65, 75, 76, 85, 88, 91
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OFFSET

1,2


COMMENTS

The decompositions need not be unique. E.g., for a(7) either 1/12 or 1/20 + 1/30 may be used in the decomposition indifferently.
For prime numbers p and any fixed epsilon < 1, a(p) > epsilon*p*log(p) for all sufficiently large p.


LINKS

Table of n, a(n) for n=1..17.
Javier Múgica, Unitary decompositions providing the terms a(n) for each n, plus a decomposition for n=18 showing that a(18)<=100.
Javier Múgica, Values of a(n)/n.


EXAMPLE

1 = 1/3 + 1/4 + 1/6 + 1/10 + 1/12 + 1/15, and there is no such decomposition starting at 1/3 and having a greatest denominator smaller than 15, so a(3)=15.


CROSSREFS

Cf. A192881, which looks at decompositions with the least possible number of terms. Those from this sequence achieve those bounds up to a(7), with exception of a(3). However, n=7 is likely the last value of n for which this holds.
Cf. A272083.
Sequence in context: A280719 A282173 A045848 * A044439 A128253 A020886
Adjacent sequences: A294648 A294649 A294650 * A294652 A294653 A294654


KEYWORD

nonn,more,nice


AUTHOR

Javier Múgica, Nov 06 2017


STATUS

approved



